Some Generalizations of the Problem of Distinct Representatives
- 1 January 1958
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 10, 230-241
- https://doi.org/10.4153/cjm-1958-027-8
Abstract
If S 1, S 2, S 3, … , S n are subsets of a set M then it is known that a necessary and sufficient condition that it is possible to choose representatives at such that ai is in S i for (i = 1, 2, 3, … , n) and such that ai ≠ aj for i ≠ j , is that for k = 1, 2, 3, … , n, the union of any k of the sets S1, S 2, … , S n, contains at least k elements. The theorem has a number of consequences amongst which we list the following.Keywords
This publication has 1 reference indexed in Scilit:
- The variation of the spectrum of a normal matrixDuke Mathematical Journal, 1953